How do you find the domain and range of #g(x)=8/(8-3x)#?

1 Answer
Jim G.
Feb 2, 2018

#x inRR,x!=8/3#
#y inRR,y!=0#

Explanation:

The denominator of g(x) cannot be zero as this would make g(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

#"solve "8-3x=0rArrx=8/3larrcolor(red)"excluded value"#

#rArr"domain is "x inRR,x!=8/3#

#(-oo,8/3)uu(8/3,+oo)larrcolor(blue)"in interval notation"#

#"to find the range rearrange making x the subject"#

#y=8/(8-3x)#

#rArry(8-3x)=8#

#rArr8y-3xy=8#

#rArr-3xy=8-8y#

#rArrx=(8-8y)/(-3y)#

#"the denominator cannot equal zero"#

#rArry=0larrcolor(red)"excluded value"#

#rArr"range is "y inRR,y!=0#

#(-oo,0)uu(0,+oo)larrcolor(blue)"in interval notation"#
graph{8/(8-3x) [-10, 10, -5, 5]}

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